Voltage's effect on magnetic rotation

I set up an experiment where I drove a solenoid with an H-bridge circuit at one voltage, and then I repeated the experiment with a higher voltage. There was a magnet positioned above the solenoid such that it was free to oscillate side to side (see picture). My observation was this: with the same driving frequency, the same duty cycle, and same overall setup, it appeared as if the magnet was oscillating faster when the higher voltage was applied.

Can someone help me to understand what I may have been seeing? My understanding of the physics of this situation led me to believe that I should have see it rotate at the same frequency as I was driving the coil regardless of the voltage applied, but it should have moved farther with each oscillation. Did I just imagine that I was seeing it move more quickly? What is voltage's effect on the rotation of a magnet in a solenoid?

the magnet has inertia so the stronger field will give it a higher frequency. a simple analogy is to consider a spring and simple harmonic motion. the frequency is the well known ω=√k/m where k is the spring constant and m is the mass of the bob on the spring. In your case, you can think of the field strength as a "spring constant" (in no way is this a formula for the real frequency, it's just a useful analogy) and m the mass of the magnet. you can see that a stronger field would lead to higher frequency.

the magnet has inertia so the stronger field will give it a higher frequency. a simple analogy is to consider a spring and simple harmonic motion. the frequency is the well known ω=√k/m where k is the spring constant and m is the mass of the bob on the spring. In your case, you can think of the field strength as a "spring constant" (in no way is this a formula for the real frequency, it's just a useful analogy) and m the mass of the magnet. you can see that a stronger field would lead to higher frequency.

Thanks for the analogy, it does help to understand from a high level why I'm seeing this, but I'd like to understand more detail (links to further reading would be excellent if you don't care to type it all out). Is there a formula for the real frequency based on magnetic field strength, magnet mass, etc? Would the "inertial frequency" (for lack of a better term) serve in the equation as a modifier of the base frequency I was driving the solenoid at? Or does the frequency at which I drive the coil have nothing to do with the motion of the magnet?

What would be the important characteristics to consider when looking at the frequency of oscillation? I don't think it's worth exploring a single setup if it will all change with the next, but from a high level is it at all fair to say that the stronger the magnetic field, the faster the oscillation of the magnet? So instead of increasing the voltage I could have also increased the number of windings on the coil to achieve the same effect?

you will always see an increased oscillation for a stronger current on the same magnet. more coils doesn't effect that, it will only make the field stronger in both cases. i should point out here that the magnetic field is not what is making the magnet rotate, it's the e-field induced by the magnetic field. magnetic fields do no work and could not be responsible for the rotation of the magnet

Is it the frequency of the oscillations that is increasing, or the amplitude of each oscillation?

In my setup, it was the frequency of the oscillations that appeared to have increased. cpsinkule's logic is beginning to make sense as to why I'm seeing the increase in frequency, but I'm clearly no electrophysicist. I'm also starting to look at it from the opposite standpoint: that of a simple generator. In that case, the faster the magnet spins, the higher the induced voltage in the coil. Therefore, I suppose it ought to work the same in reverse. I would never have suspected that inertia was a key player in this interaction though!

you should be careful here. the inertia of the magnet has no effect on what current it would generate in a loop. a 1 ton magnet with the same field strength as a 1 gram magnet would produce an equal current through a given loop assuming you moved them at the same pace

What is the frequency of the coil compared to the frequency of the oscillations?

The frequency of the coil was set at 260Hz for this particular experiment. I didn't have a good way of quantifying the frequency of oscillations, but I would estimate it increased by half when I increased the voltage (from 500Hz to 750Hz would be my best guess). The voltage was increased from 2.5 to 3.8V.

you should be careful here. the inertia of the magnet has no effect on what current it would generate in a loop. a 1 ton magnet with the same field strength as a 1 gram magnet would produce an equal current through a given loop assuming you moved them at the same pace

Thanks for the warning. So in the case of the generator, the current generated is a factor of the magnetic field strength (and the resultant emf across the coil is generated due to the current flow), whereas the work done on the magnet in my "motor" is due to a magnetic field inducing an e-field on the magnet?

The current generated by a magnet in a loop of wire depends on something called the "flux" of the magnetic field through a surface attached to the loop of wire. To be specific, it depends on the rate of change of this flux. Loosely speaking it depends on several things, how many coils, how fast the magnetic field is changing (ie how fast you move the magnet), and how large the coils are. The work done on the magnet is due to whatever source is producing a current in your coil, be it a battery or the power plant supplying electricity to your house. The electric field is induced by a changing magnetic field, and the changing magnetic field is induced by the current in the coil, which in turn is produced by your power supply.